This year in math class we used a math program called Connected Mathematics 2. Connected Mathematics 2 is made up of eight units, each organized around an important math idea or a collection of related ideas. So far we have covered six out of the eight units. The units we covered are Prime Time, Bits and Pieces 1, Bits and pieces 2, Shapes and Designs, Covering and Surrounding, and How Likely is it?. As we work through each investigation we build strategies by solving problems and discussing our solutions. We record our work in our note books, which are set up to help us organize the information. Our note books are divided into four sections. The class work section has all the problems we do in class. The homework section has ACE, and other homework. The assessments section holds our tests, quizzes, reflections, and RAP sheets. And the reference section has the information that we need to look back on.
Each book starts off with three problems. The problems are an example of what we will face in the unit. The problems point out the ideas we will investigate, and the ideas, will show up in later problems, or ACE Homework. ACE stands for Applications, Connections, and Extensions.
Each unit provides a set of goals, or Mathematical Highlights, that preview the important ideas of the unit. It is a good place to look to help understand what the main idea of the unit is.
Each unit is divided into investigations. The investigations each focus on certain skills. Each unit involves at least three investigations. Each investigation is broken up into three to five problems. We do the problems individually, in groups, or as a class. At the end of each investigation we have to think about what we learned and answer several questions. The questions are called reflections. We did all these things in Connected Mathematics 2.
Reflection example: Book: Prime Time page: 60 Investigation: 4 Reflection number: 4 Date: 10/4/2011
1 a. Not every number has a prime factorization because 1 doesn’t have any prime factors.
b. A number can only have one prime factorization because a prime factorization is the longest factor string.
c. It is important that 1 is not a prime number because prime factor strings would go on forever.
2 a. You can use the prime factorization of two numbers to find out their least common multiple by finding out the shortest factor string that contains the prime factor factorization of both numbers.
b. You can use the prime factorization of two numbers to find their greatest common factor by multiplying the prime factors that are common to both prime factorizations. An example of this is 24 and 60 because they both have 2x2x3 as prime factorization strings. If you multiply 2x2x3 you get 12 their greatest common factor.
c. You can use the prime factorization of two numbers to find out if they are relatively prime by looking at the prime factorization of the two numbers if they have no prime common factors. 7 and 9 are examples.
3 If the greatest common factor of two numbers is 1 then the least common multiple will be the product of the two numbers.
This year in math class we used a math program called Connected Mathematics 2.
Connected Mathematics 2 is made up of eight units, each organized around an important math idea or a collection of related ideas. So far we have covered six out of the eight units. The units we covered are Prime Time, Bits and Pieces 1, Bits and pieces 2, Shapes and Designs, Covering and Surrounding, and How Likely is it?.
As we work through each investigation we build strategies by solving problems and discussing our solutions. We record our work in our note books, which are set up to help us organize the information. Our note books are divided into four sections. The class work section has all the problems we do in class. The homework section has ACE, and other homework. The assessments section holds our tests, quizzes, reflections, and RAP sheets. And the reference section has the information that we need to look back on.
Each book starts off with three problems. The problems are an example of what we will face in the unit. The problems point out the ideas we will investigate, and the ideas, will show up in later problems, or ACE Homework. ACE stands for Applications, Connections, and Extensions.
Each unit provides a set of goals, or Mathematical Highlights, that preview the important ideas of the unit. It is a good place to look to help understand what the main idea of the unit is.
Each unit is divided into investigations. The investigations each focus on certain skills. Each unit involves at least three investigations. Each investigation is broken up into three to five problems. We do the problems individually, in groups, or as a class. At the end of each investigation we have to think about what we learned and answer several questions. The questions are called reflections.
We did all these things in Connected Mathematics 2.
Reflection example:
Book: Prime Time page: 60 Investigation: 4 Reflection number: 4 Date: 10/4/2011
1 a. Not every number has a prime factorization because 1 doesn’t have any prime factors.
b. A number can only have one prime factorization because a prime factorization is the longest factor string.
c. It is important that 1 is not a prime number because prime factor strings would go on forever.
2 a. You can use the prime factorization of two numbers to find out their least common multiple by finding out the shortest factor string that contains the prime factor factorization of both numbers.
b. You can use the prime factorization of two numbers to find their greatest common factor by multiplying the prime factors that are common to both prime factorizations. An example of this is 24 and 60 because they both have 2x2x3 as prime factorization strings. If you multiply 2x2x3 you get 12 their greatest common factor.
c. You can use the prime factorization of two numbers to find out if they are relatively prime by looking at the prime factorization of the two numbers if they have no prime common factors. 7 and 9 are examples.
3 If the greatest common factor of two numbers is 1 then the least common multiple will be the product of the two numbers.
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